Abstract
Euler type analysis usually used for compression members in structural engineering does not work for railroad track. Euler type analytical formulas for horizontal and vertical buckling endorsed in a recent literature is reviewed to demonstrate its weakness. Using definition of moment and curvature as well as principle of equilibrium, the author suggests formula for horizontal buckling load of railroad track and demonstrates validation in context with currently accepted values, published results, and past field tests. The buckling load from suggested formula agrees with the recent buckling load formula based on total energy theorem. A formula is suggested to study the effect of misalignment on critical temperature differential or critical load. A vertical buckling load formula is derived from horizontal buckling load formula. A buckling process is narrated through step by step computation. Formulas are suggested to compute the effect of track misalignment on critical buckling load and threshold radius of a vertical curve.
Highlights
In terms of analysis, buckling in a railroad track is a quite complex phenomenon due to the following: s The ‘‘end’’ conditions of the rails are neither perfectly fixed nor perfectly pinned nor free, but provide varying rotational and lateral resistance depending on numerous factors, s Resistance to lateral displacement is provided by the lateral stiffness of rails, track frame, and ballast resistance, s Railroad track invariably contains initial curvature and imperfections, s Axial loading through the centroid of the track would seldom occur etc
DTc = 800C if the lateral resistance, FQVW is reduced by 50%; this implies that a track would not buckle at above 100°C even if all ballast above tie-ballast interface is removed
There is an analytical formula with a calculation example for computing critical temperature differential for vertical buckling in literature as follows[3,13]: sffiffiffiffiffiffiffiffiffiffiffiffi
Summary
In terms of analysis, buckling in a railroad track is a quite complex phenomenon due to the following:. The aforementioned seven field tests yield a critical temperature differential of 42.5°C to 50°C corresponding to a track buckling load of 173 to 200 tons; the lower buckling load was observed on test tracks with geometric imperfection It appears that tie type does not influence buckling load. A published value from Table 1 shows 49°C (cf 49°C on first row in Table 2) as critical temperature differential for horizontal buckling with wood tie and 47 kg/m rail.[3,11] No value is given for concrete tie. A relation between critical vertical misalignment and critical vertical buckling load may be expressed from the equation (16) replacing lateral resistance term, FQVW by the weight of track, w (N/cm) and moment of inertia, I (Iy-y) term by Ix-x as under: 2wEIxÀx 107P2c ð28Þ.
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